Influence of the basins of attractions in the register jumps of the clarinet

TL;DR

This paper investigates how the basins of attraction influence register transitions in clarinet playing, combining numerical simulations with analysis of stability regions to better understand register jumps.

Contribution

It introduces a numerical approach to analyze the influence of basins of attraction on register jumps during clarinet play, highlighting the role of initial conditions and timing.

Findings

The stability range of the second register is narrower when opening the register hole during first register sound.

The probability of reaching the second register depends on the basin of attraction structure.

Timing of hole opening affects the likelihood of successful register transition.

Abstract

When playing the clarinet, opening the register hole allows for a transition from the first to the second register, producing a twelfth interval. On an artificial mouth, the blowing pressure range where the second register remains stable can be determined by gradually varying the blowing pressure while keeping the register hole open. However, when the register hole is opened while the instrument is already producing the first register, the range of blowing pressures that lead to a stable second register is narrower than the full stability zone of the second register. This phenomenon is investigated numerically by performing multiple hole openings at different times for each blowing pressure value. The evolution of the probability of reaching the second register is computed, and its relationship with the structure of the basin of attraction of the second register is analyzed.